Will the curvature be just right to bring the wave function to zero as x goes to infinity. Only with exactly the right initial conditions
Means that ψ ( x ) tends to diverge to infinity.
Potential V ( x ) = V 0 E , the curvature is always away from the axis. The simplest example is that of a constant In bothĬases, ψ ( x ) is always curving towards the x -axis - so, for E > V ( x ), ψ ( x ) has a kind of stability: its curvature isĪlways bringing it back towards the axis, and so generating oscillations. This means that if E > V ( x ) , for ψ ( x ) positive ψ ( x ) is curving negatively, for ψ ( x ) negative ψ ( x ) is curving positively. Rate of change of slope, is the curvature – so the curvature of the function is Curvature of Wave Functionsĭ 2 ψ ( x ) d x 2 = 2 m ( V ( x ) − E ) ℏ 2 ψ ( x )Ĭan be interpreted by saying that the left-hand side, the Previous index next PDF Schrödinger’s Equation in 1-D: Some Examples
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